Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.